Method for detecting particulate radiation

ABSTRACT

When detecting particulate radiation, such as electrons, with a pixelated detector, a cloud of electron/hole pairs is formed in the detector. Using the signal caused by this cloud of electron/hole pairs a position of the impact is estimated. When the size of the cloud is comparable to the pixel size, or much smaller, the estimated position shows a strong bias to the center of the pixel and the corners, as well to the middle of the borders. This hinders forming an image with super-resolution. By shifting the position or by attributing the electron to several sub-pixels this bias can be countered, resulting in a more truthful representation.

The invention relates to a method of detecting particulate radiationusing a semiconductor based pixelated detector, the detector pixelshaving a detector pixel size, the detector sensitive to the particulateradiation, each particle of the particulate radiation causing amultitude of electron/hole pairs in the semiconductor material of thedetector, the multitude of electron/hole pairs having a centroid and acentroid extent, the extent of the centroid larger than the detectorpixel size, the method comprising:

-   -   A step of intercepting a particle of the particulate radiation,    -   A step of estimating the number of electron/hole pairs for a        number of adjacent detector pixels,    -   A step of estimating the position of the centroid of the number        of electron/hole pairs using the estimates of electron/hole        pairs in adjacent detector pixels,    -   A step of estimating the impact position of the particle using        said estimated position of the centroid,    -   A step of forming a pixelated image using the estimated position        of a multitude of estimated impact positions, the pixelated        image consisting of image pixels having an intensity,

Such a method is known inter alia from the “K2 Direct DetectionCameras”, commercially available from Gatan Inc., 5794 W. Las PositasBlvd., Pleasanton, Calif. 94588, USA.

The known method describes a pixelated detector intercepting radiationin the form of energetic electrons. Each intercepted electron causes acloud of electron/hole pairs in the semiconductor material of thedetector, thereby causing a signal in the detector pixel(s) where it isdetected. As the diameter of the cloud (the centroid) is larger than thediameter of the detector pixels, one impinging electron causes a signalin multiple detector pixels. Using the signal of different detectorpixels, an estimate of the impact position is determined with aresolution better than the detector's pixel size, in this case with aresolution of half a detector pixel diameter. This is used to form animage with super-resolution (as the resolution is better than thedetector pixel size).

The method does not disclose how the impact position is determined orestimated. The method has not proven to give results for a resolutionother than half a detector pixel or a (multiple of a) whole detectorpixel.

It is noted that in many cases the extent of the centroid can becharacterized with a FWHM (Full Width at Half Maximum) diameter.

The invention intends to provide a method with improved resolutionand/or signal-to-noise (S/N) ratio compared to the known method.

To that end the method is characterized in that when estimating theimpact position said estimate has a position dependent bias depending onthe position within the detector pixel, and the contribution of eachestimated impact position to corresponding image pixels is adjusted tocounter the effect of said position dependent bias.

Inventors found that the response of a detector pixel to an impingingparticle not only depends on different responses between pixels(inter-pixel differences or inter-pixel non-uniformity), but that whenestimating the position within the detector pixel the probability that aparticle is allocated to a position on the detector pixel (the positiondependent bias) is non-uniform: said position dependent bias depends(reproducibly) on the position on the detector pixel and thus introducesan intra-pixel non-uniformity).

This can be explained as follows: assume that the extent of the cloud ofelectron/hole pairs is smaller than the pixel size, then if the adjacentdetector pixels show no electron/hole pairs (all electron/hole pairs aregenerated within one detector pixel) the position will be allocated tothe middle of the detector pixel, as there is no ground to allocate itto another position. Only when the particle hits near the border betweentwo detector pixels (thus causing electron/hole pairs in two detectorpixels) a position near the border can be determined, but where alongthe border is unknown: therefore the position of the particle will beassociated to the middle of the border. Only near the corners a truepositioning in two directions can be performed. For an extent muchlarger than the detector pixel size the effect (non-uniformity) smearsout. For a centroid size (slightly) larger than the pixel size, theestimated positions cluster near the center of the detector pixel, to alesser extent to the center of the borders, and to the corners.

Inventors experimented to find a solution to counter the effect of saidposition dependent bias. The most obvious solution coming to mind of theskilled artisan is to attach a lower probability to the events near thepeaks. In an image this is realized by scaling the intensity of imagepixels corresponding to high probability locations. However, this has nophysical basis: such scaling implies that only part of a particledetected at the position with a high probability is imaged. Also, partof the information is lost, resulting in an increase in noise. Themethod according to the invention, with or without improved resolution,can also be used for improved S/N ratio near the Nyquist frequency (theNyquist frequency governed by the detector pixel size).

Inventors found that by adjusting the contribution of each impactposition to corresponding image pixels to counter the effect of saidposition dependent bias, the effect of the position dependent bias canbe countered.

The contribution of each estimated impact position to correspondingimage pixels may comprise the adjustment of the estimated positionwithin the detector pixel, the adjustment a function of the estimatedposition within the detector pixel. This may be achieved using amathematical function, preferably a spline function, or using a look-uptable (LUT). When using a LUT, the adjustment of the position may bebased on one LUT value, or on an interpolation of more than one LUTvalues. This results in an adjusted estimated position.

Alternatively or additionally the contribution of each estimated impactposition to corresponding image pixels may comprise adding intensity tomore than one image pixels, the adding a function of the estimatedposition (or adjusted estimated position) within the detector pixel.

The adding of intensity to more than one image pixel may be derivedusing a LUT, the LUT values a function of the estimated position withinthe pixel. The LUT may show a large number of values, each valuecorresponding to a rounded estimated position. This introduces a (small)rounding in positional information. Preferably the values are derivedfrom an interpolation in the LUT, the interpolation based on theestimated position within the detector pixel. Less rounding is then tobe expected. Alternatively the adding of intensity may be derived from amathematical function, preferably a spline function.

In yet another embodiment the particulate radiation is particulateradiation from the group of electrons, ions, and X-rays

It is noted that the invention does not relate to PALM or dSTORM, asthese super-resolution methods detect a multitude of particles capturedby one pixel, each particle a photon of visible light, each photoncausing (at most) one electron/hole pair, followed by determining thecentroid of several adjacent pixels.

It is further noted that for Gatan's S2 camera the only knownsuper-resolution setting is half the pixel size. Nowhere does Gatandisclose that the estimated position is shifted to counter clustering athalf the pixel size. As the position dependent bias error introduces anon-uniformity at twice the pixel size, this is hard to detect when thesuper-resolution is set to exactly half the pixel size

The method is compatible with particulate radiation from the group ofelectron, ions, and X-ray photons.

In an embodiment the method further comprises obtaining a pixelatedimage using the estimates of the impact position of a multitude ofparticles, the estimate of the impact position of each particlecontributing to the intensity of several image pixels.

It is noted that when attributing the detected particle to only onepixel of the image, Moiré effects and interferences can occur. Inventorsfound that to avoid this, the contribution of each particle is bestspread out over several pixels.

It is noted that as long as the point spread function (PSF) used tospread out the contribution is known, this is a reversible method andthe original position can be derived by deconvolution of the imageintensities and the (known) PSF.

Preferably the several image pixels are adjacent image pixels, but theamount of pixels need not be limited to the image pixels directlybordering the pixel corresponding to the estimated impact position.

It is noted that although particularly useful for the method of theinvention, also other methods for detecting particulate radiation maybenefit from obtaining a pixelated image using the estimates of theimpact position of a multitude of particles, the estimate of the impactposition of each particle contributing to the intensity of several imagepixels.

The invention is now elucidated using FIG. 1.

To that end FIG. 1 schematically shows the position dependent biasacross the pixel. This concerns actual measurements where a large numberof electrons impacted on a pixelated detector, the pixelated detectorhaving a pixel size of 14×14 μm², while the FWHM size of the cloud ofelectron/hole pairs is estimated to be 22 μm (1.6 times the pixel size).Note that the irradiation was uniform. Clearly the estimated position isnot uniform, indicating that there is a position dependent bias. Thisposition dependent bias can be countered by shifting of the position,using a vector field for each sub-pixel, or using a function where theadjusted position (u,v) is a function of the detected position (x,y),thus (u,v)=F(x,y), or it can be countered by spreading the contributionof one event (impact) over several image pixels or sub-pixels(representing the impact position as a ‘blob’ contributing to severaldetector sub-pixels, the blob a position dependent blob. It is notedthat one sub-pixel may show a one-to-one relation to an image pixel, orseveral sub-pixels may contribute to one image pixel. In any event it isfavorable to spread the information representing one estimated impact isspread over several image pixels. This spreading over several imagepixels (further referred to as spreading) is in itselfcounter-intuitive, as it gives a result similar to blurring, but thespreading eliminates (or greatly reduces) Moiré-effects andinterferences.

It is noted that when using appropriate spreading, and assuming theimage is a sparse image (so: in most cases one or no impacts per imagepixel) the estimated impact positions can be perfectly retrieved fromthe image, that is: no positional information is lost. In case of anon-sparse image the positional information of each individual estimatedimpact cannot be retrieved, but the information is incorporated in theimage.

It is further noted that this spreading (effectively a spatial low-passfilter) may be followed by a high-pass filter to improve the imagequality (crisp the image) with minimal loss of information.

The shifting and/or spreading should take place before attributing theinformation to an image pixel. When the spreading is done aftercombining detector images, information is lost. Shifting after combiningis not possible. From this inventors concluded that any correctionshould be performed on the level where single impact events are handled,ideally by shifting the estimated impact position and spreading theinformation over several image pixels. A similar (although slightlyinferior) result can be achieved when the impact is attributed to agroup of detector sub-pixels (the sub-pixels used to construct an image)or a group of image pixels.

If the shift or the spreading is performed with a higher resolution thanthe image representation, the high-frequency information (for exampleabove half of the Nyquist frequency) is better represented, resulting inan improved S/N ratio.

It is noted that all this does not take away the need to correct forbefore mentioned inter-pixel differences.

Summarizing, when detecting particulate radiation, such as electrons,with a pixelated detector, a cloud of electron/hole pairs is formed inthe detector. Using the signal caused by this cloud of electron/holepairs a position of the impact is estimated. Inventors found that, whenthe size of the cloud is comparable to the pixel size, or much smaller,the estimated position shows a strong bias to the center of the pixeland the corners, as well to the middle of the borders. This hindersforming an image with super-resolution. By shifting the position or byattributing the electron to several sub-pixels this bias can becountered, resulting in a more truthful representation. It is noted thatshifting and/or spreading should take place before attributing theinformation to an image pixel, and before adding the events persub-pixel.

When the spreading is done after combining detector images, informationis lost. It is noted that shifting after combining detector images isnot possible.

1. A method of detecting particulate radiation using a semiconductorbased pixelated detector, the detector pixels having a detector pixelsize, the detector sensitive to the particulate radiation, each particleof the particulate radiation causing a multitude of electron/hole pairsin the semiconductor material of the detector, the multitude ofelectron/hole pairs having a centroid and a centroid extent, the extentof the centroid extent larger than the detector pixel size, the methodcomprising: intercepting a particle of the particulate radiation,estimating the number of electron/hole pairs for a number of adjacentdetector pixels, estimating the position of the centroid of the numberof electron/hole pairs using the estimates of electron/hole pairs inadjacent detector pixels, estimating the impact position of the particleusing said estimated position of the centroid, said estimated impactposition having a position dependent bias depending on the positionwithin the detector pixel, forming a pixelated image using the estimatedposition of a multitude of estimated impact positions, the pixelatedimage consisting of image pixels having an intensity, and adjusting thecontribution of each estimated impact position to corresponding imagepixels to counter the effect of said position dependent bias.
 2. Themethod of claim 1 in which the adjustment of the contribution of eachestimated impact position to corresponding image pixels comprises theadjustment of the estimated position, the adjustment a function of theestimated impact position relative to the detector pixel.
 3. The methodof claim 1 in which the adjustment of the contribution of each estimatedimpact position to corresponding image pixels comprises adding intensityto more than one image pixel.
 4. The method of claim 2 in which thefunction is a function from the group of spline functions.
 5. The methodof any of claim 2 in which the function is stored in a look-up table(LUT).
 6. The method of any of claim 1, in which the particulateradiation is particulate radiation from the group of electrons, ions,and X-rays.
 7. The method of claim 2, in which the adjustment of thecontribution of each estimated impact position to corresponding imagepixels comprises adding intensity to more than one image pixel.
 8. Themethod of claim 3, in which the function is a function from the group ofspline functions.
 9. The method of claim 3, in which the function isstored in a look-up table (LUT).
 10. The method of claim 2, in which theparticulate radiation is particulate radiation from the group ofelectrons, ions, and X-rays.
 11. The method of claim 3, in which theparticulate radiation is particulate radiation from the group ofelectrons, ions, and X-rays.
 12. The method of claim 4, in which theparticulate radiation is particulate radiation from the group ofelectrons, ions, and X-rays.
 13. The method of claim 5, in which theparticulate radiation is particulate radiation from the group ofelectrons, ions, and X-rays.